Referring to FIG. 1 of the drawings, the reference numeral 100 generally designates a conventional voltage controlled oscillator (VCO). The VCO 100 is generally comprised of an oscillator tank, a pair of cross-coupled NMOS FETs Q1 and Q2 (which operate as amplifiers having transconductances of gm), and a current source 102. Each of the FETs Q1 and Q2 has its gate coupled to the drain of the other FET Q1 and Q2, and the drain of each of the FETs Q1 and Q2 is coupled to the oscillator tank. The oscillator tank is generally comprised of inductors L1 and L2 (which generally have equal values) and capacitors C1 and C2 (which are variable capacitors).
In operation, VCO 100 is able to generate an output signal with a frequency that is generally proportional the current through current source 102 and the output resistance. The phase noise would, thus, be as follows:
                                          P            ⁢                                                  ⁢            N                    =                                                                                          i                    2                                    _                                ⁢                                  R                  P                  2                                                            2                ⁢                                  V                  OUT                  2                                                      ⁢                                          (                                                      ω                    0                                                        2                    ⁢                                          Q                      0                                        ⁢                    Δ                    ⁢                                                                                  ⁢                                          ω                      0                                                                      )                            2                                      ,                            (        1        )            where i2 is the equivalent output current noise, Q0 is the loaded quality factor, RP is the output resistance, and VOUT is the output voltage. Specifically, for a steady state oscillation, the average transconductance (gm) is approximately equal to the inverse of resistance RP (gm=1/RP). Under these steady state conditions, equivalent output current noise i2 is as follows:
                                                        i              2                        _                    =                                                                      4                  ⁢                  kT                                                  R                  p                                            +                              4                ⁢                kT                ⁢                                                                  ⁢                γ                ⁢                                                                  ⁢                                  g                  m                                                      =                                          4                ⁢                                  kT                  ⁡                                      (                                          1                      +                      γ                                        )                                                                              R                p                                                    ,                            (        2        )            where the first term corresponds to tank resistance and the second term corresponds to the active device. By substituting Equation (2) into Equation (1), the phase noise PN can be represented as follows:
                              P          ⁢                                          ⁢          N                =                                                            4                ⁢                                  kT                  ⁡                                      (                                          1                      +                      γ                                        )                                                  ⁢                                  R                  p                                                            2                ⁢                                  V                  OUT                  2                                                      ⁢                                          (                                                      ω                    0                                                        2                    ⁢                                          Q                      0                                        ⁢                    Δ                    ⁢                                                                                  ⁢                                          ω                      0                                                                      )                            2                                =                                                    4                ⁢                                  kT                  ⁡                                      (                                          1                      +                      γ                                        )                                                  ⁢                                  R                  p                                                            2                ⁢                                                      (                                                                  kI                        AVE                                            ⁢                                              R                        p                                                              )                                    2                                                      ⁢                                                            (                                                            ω                      0                                                              2                      ⁢                                              Q                        0                                            ⁢                      Δ                      ⁢                                                                                          ⁢                                              ω                        0                                                                              )                                2                            .                                                          (        3        )            Thus, it can be seen from this conventional VCO 100 that that improving the phase noise characteristics can be accomplished through increasing the quality factor Q of the oscillator tank or optimization of related device properties in the VCO 100.
Some examples of conventional circuits are: U.S. Patent Pre-Grant Publ. No. 2008/0143446; U.S. Patent Pre-Grant Publ. No. 2008/0150644; and Hegazi et al., “A filtering technique to lower LC oscillator phase noise,” IEEE Journal of Solid State Circuits, Vol. 36, No. 12, December 2001.